28. A ball of mass (m) 0.5 kg is attached to the end of a string having length (L) 0.5 m . The ball is rotated on a horizontal circular path about vertical axis. The maximum tension that the string can bear is 324 N . The maximum possible value of angular velocity of ball (in radian/s) is [Figure]
(A) 9
(B) 18
(C) 27
(D) 36

ANSWER: D

1. A meter bridge is set-up as shown, to determine an unknown resistance ' $X$ ' using a standard 10 ohm resistor. The galvanometer shows null point when tapping-key is at 52 cm mark. The end-corrections are 1 cm and 2 cm respectively for the ends A and B . The determined value of ' $X$ ' is [Figure]
   (A) 10.2 ohm
   (B) 10.6 ohm
   (C) 10.8 ohm
   (D) 11.1 ohm

ANSWER:B

1. A $2 \mu \mathrm {~F}$ capacitor is charged as shown in figure. The percentage of its stored energy dissipated after the switch $S$ is turned to position 2 is [Figure]
   (A) $0 \%$
   (B) $20 \%$
   (C) $75 \%$
   (D) $80 \%$

ANSWER: D

SECTION - II (Total Marks : 16)

(Multiple Correct Answers Type)

This section contains 4 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE may be correct.

A body of mass $\mathrm { m } = 10 \mathrm {~kg}$ is attached to one end of a wire of length 0.3 m . What is the maximum angular speed (in $\mathrm { rad } \mathrm { s } ^ { - 1 }$ ) with which it can be rotated about its other end in a space station without breaking the wire? [Breaking stress of wire $( \sigma ) = 4.8 \times 10 ^ { 7 } \mathrm {~N} \mathrm {~m} ^ { - 2 }$ and area of cross-section of the wire $= 10 ^ { - 2 } \mathrm {~cm} ^ { 2 }$ ]

A boy ties a stone of mass 100 g to the end of a 2 m long string and whirls it around in a horizontal plane. The string can withstand the maximum tension of 80 N . If the maximum speed with which the stone can revolve is $\frac { K } { \pi } \mathrm { rev } \min ^ { - 1 }$. The value of $K$ is : (Assume the string is massless and un-stretchable)
(1) 400
(2) 300
(3) 600
(4) 800

A ball of mass 0.5 kg is attached to a string of length 50 cm. The ball is rotated on a horizontal circular path about its vertical axis. The maximum tension that the string can bear is 400 N. The maximum possible value of angular velocity of the ball in rad $\mathrm { s } ^ { - 1 }$ is,:
(1) 1600
(2) 40
(3) 1000
(4) 20